lra detection

研究生：研究生：

指導教授：指導教授：

StudentStudent ：：

AdvisorAdvisor ：：

LRA LRA DetectionDetection

魏學文魏學文

林忠良林忠良 Harmoko H. R.Harmoko H. R.

Prof. S-W Wei

Presentation Date: April 16, 2009Presentation Date: April 16, 2009

http://163.22.24.50/

OutlineOutline

System Model Conventional Detection Schemes Lattice Reduction (LR) LR Aided Linear Detection Simulation Results Conclusions

22

2009/04/162009/04/16

http://163.22.24.50/

System ModelSystem Model

2009/04/162009/04/16

33

where H=[h1,…,hM], representing a flat-fading channel

n+Hx=y

x1

Mapper S/P Detector P/S Demapper

xM

y1

yN

DataEstimated

Data

h1,M

n1

nN

hN,1

h1,1

Transmitter Receiver

hN,M

System model of a MIMO system with M transmit and N received antennas

The received signal vector y can be represented as

http://163.22.24.50/

Conventional Detection SchemesConventional Detection Schemes

Maximum likelihood (ML) detector

Since ML requires computing distances to every codeword to find the closest one, it has exponential complexity in transmission rate.

Linear detectorTake form of , where A is some matrix

Q(.) is a slicer

Zero forcing detector

A = H+ where (.)+ is pseudoinverse operation

Problem: ZF performance suffer dramatically due to noise enhancement if H is near singular.

44

2minargˆ Hxyxx

ML

Ayx Qˆ

nHHxHyHx ~

2009/04/162009/04/16

http://163.22.24.50/

Minimum mean square estimator (MMSE) detector

A = ( HHH + σn2I )-1HH

The transmitted vector can be estimated by

where is the extended channel matrix and is the extended received vector

55

Conventional Detection SchemesConventional Detection Schemes

2009/04/162009/04/16

yHyHIHHx n HH 2~

H y

I

HH

n

1,m0

yyand

http://163.22.24.50/

Lattice ReductionLattice Reduction A complex lattice is the set of points

If we can find a unimodular transformation matrix T that contains only integer entries and the determinants is det(T)=±1, then

will generates the same lattice as the lattice generated by

The aim of lattice reduction is to transform a given basis H into a new basis with vectors of shortest length or, equivalently, into a basis consisting of roughly orthogonal basis vectors.

66

GL k

M

kkk xhxH

1

HTH ~

H~

H

unimodular isand ~~

THTHHH LL

H~

2009/04/162009/04/16

http://163.22.24.50/

Lattice ReductionLattice Reduction To describe the impact of this transformation, we introduce the

condition number :

к(H) = σmax/σmin ≥1

where σmax = largest singular value

σmin = smallest singular value

Usually, is much better conditioned than H, therefore leads to less noise (interference) enhancement for linear detection, this is the reason why LR can help the detector to achieve better performance.

Lenstra-Lestra Lovasz (LLL) reduction algorithm can help us finding the transformation matrix T.

77

H~

2009/04/162009/04/16

http://163.22.24.50/

LLL AlgorithmLLL Algorithm

99

Definition 1 (Lenstra Lenstra Lovasz reduced ):

A basis with QR decomposition is LLL reduced with parameter , if

for all 1 ≤ l < k ≤ M … (1)

and for all 1 ≤ l < k ≤ M. … (2)

The parameter δ (1/2 < δ < 1) trade off the quality of the lattice reduction for large δ, and a faster termination for small δ.

MNCH~

RQH~~~

llkl RR ,,

~

2

1~ llkl RR ,,

~

2

1~ and

2

,1

2

,

2

1,1

~~~kkkkkk RRR

2009/04/162009/04/16

http://163.22.24.50/

LLL AlgorithmLLL Algorithm

1010

OUTPUT: a basis which is LLL-reduced with parameter δ, T satisfying QRTHTH ~

RQH~~~ 2009/04/162009/04/16

http://163.22.24.50/

LRA Linear DetectionLRA Linear Detection

1111

TX H G=H+ Slicerx̂yx

n

Block diagram of conventional ZF detector

TX T-1 H’=HTy

n

shift &scale (HT)+ T undo shift

& scale

x̂

LRA receiver operationsLRA transmitter = conventional transmitter

H

xslicer

y x̂

Block diagram of LR-ZF detector with shift & scale operation included at Receiver

*LRA: Lattice Reduction Aided

2009/04/162009/04/16

http://163.22.24.50/


1212

52d

53,51,51,53 x

2,1,0,1x

Transformed into contiguous integer and also include origin

Shift and scale operation:

2Nd 1xx HH d

Example:

The received signal vector is expressed as

n+Hx=y

2009/04/162009/04/16

http://163.22.24.50/


1313

Lattice reduction aided zero forcing (LR-ZF):

nHzyHz ~~~LRZF

LRZFLRZF Q zz ~ˆ

LRZFLRZF zTx ˆˆ

n+Hx=yshift & scale

2Ndy 1H=y

n1xHn+xH=y 2Nddn1HHx 2Nd

2Nd 1Hy

The received signal vector can be rewritten as

nzHn+xTTHn+xH=y ~1

Describe the same transmitted signal

THH ~

xTz 1

2ˆˆ NLRZFLRZF dd 1xx 2Nd 1xx

2009/04/162009/04/16

http://163.22.24.50/


1414

Lattice reduction aided MMSE (LR-MMSE):

yHIHHz H

NH

LRMMSE

~~~~ 12

yHz~~H

MMSELR

Using the extended model, LR-MMSE detector can be expressed as

2009/04/162009/04/16

http://163.22.24.50/

Simulation ResultsSimulation Results

1515

2009/04/162009/04/16

http://163.22.24.50/

ConclusionsConclusions Various MIMO detection methods that make

use of lattice reduction algorithm are discussed.

It is also shown that LRA detection perform much better than other conventional linear detector.

1616

2009/04/162009/04/16

http://163.22.24.50/

ReferencesReferences

1717

[1]D. Wubben, R. Bohnke, V. Kuhn, and K. D. Kammeyer, “Near- maximum-likelihood detection of MIMO systems using MMSE-based lattice reduction,” in Proc. 39th Annu. IEEE Int. Conf. Commun. (ICC 2004), Paris, France, June 2004, vol. 2, pp. 798-802.

[2]H. Vetter, V. Ponnampalam, M. Sandell, and P. A. Hoeher, "Fixed Complexity LLL Algorithm," Signal Processing, IEEE

Transactions on, no. 4, vol. 57, pp. 1634-1637, April, 2009.

2009/04/162009/04/16

http://163.22.24.50/

ReferencesReferences

112/04/21112/04/21

1818

THANK YOU

lra detection

Documents